This chapter presents an overview of the DISCO project's solutions to several problems in natural language pragmatics. Its central focus is on relating utterances to intentions through speech act recognition. Subproblems include the incorporation of linguistic cues into the speech act recognition process, precise and efficient multiagent belief attribution models (Corporate Agents), and speech act representation and processing using Corporate Agents. These ideas are being tested within the COSMA appointment scheduling system, one application of the DISCO natural language interface. Abductive speech act processing in this environment is not far from realizing its potential for fully bidirectional implementation.